theorem
  for f1 be PartFunc of C,REAL holds (f1 is total & f2 is total
  iff f1(#)f2 is total)
proof
  let f1 be PartFunc of C,REAL;
  thus f1 is total & f2 is total implies f1(#)f2 is total;
  assume f1(#)f2 is total;
  then dom f1 /\ dom f2 = C by Def3;
  hence dom f1 = C & dom f2 = C by XBOOLE_1:17;
end;
